Abstract group data - 972.798

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• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 6, 6], 'aut_gens': [[44475821, 22843831, 732529, 33902551, 879733], [44833571, 23091331, 53436277, 33902551, 53803441], [31445717, 23088631, 20632672, 879733, 1097596], [31930757, 22849231, 53802127, 53803441, 1097596], [22968971, 23088631, 1242019, 33902551, 879733]], 'aut_group': '7776.is', 'aut_hash': 4994213685505676867, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 60, 'aut_perms': [55851051313517162782594568271748998029500601472536474212235178164426538513183236, 1994699103317261193648898743843564535111242628738825076307092799132061320047942850, 28735516026232590182234210834959801048495348230471373775306067236249877625260489, 883251737826809002122264990504535656043576031599448350414097434256795980904054542], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 27, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 2, 1], [3, 4, 1, 1], [3, 4, 2, 2], [3, 6, 1, 1], [3, 6, 2, 1], [3, 6, 4, 1], [3, 12, 2, 3], [3, 12, 4, 2], [6, 18, 1, 1], [6, 27, 2, 1], [6, 27, 4, 1], [6, 54, 1, 1], [6, 54, 2, 2], [6, 54, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(D_4\\times D_6)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '7776.is', 'autcentquo_hash': 4994213685505676867, 'autcentquo_nilpotent': False, 'autcentquo_order': 7776, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(D_4\\times D_6)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 27, 2], [3, 2, 3], [3, 3, 2], [3, 4, 5], [3, 6, 7], [3, 12, 14], [6, 18, 1], [6, 27, 6], [6, 54, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '972.798', 'commutator_count': 1, 'commutator_label': '81.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 798, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 27, 1, 2], [3, 2, 1, 3], [3, 3, 2, 1], [3, 4, 1, 3], [3, 4, 2, 1], [3, 6, 1, 1], [3, 6, 2, 3], [3, 12, 1, 2], [3, 12, 2, 6], [6, 18, 1, 1], [6, 27, 2, 3], [6, 54, 1, 3], [6, 54, 2, 3]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 12, 'exponent': 6, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '324.167', 'hash': 798, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 3, 6, 3, 3], 'inner_gens': [[44475821, 23088631, 735229, 1097596, 879733], [1220891, 22843831, 732529, 33902551, 879733], [44470421, 22843831, 732529, 1097596, 53803441], [44836271, 22843831, 1101079, 33902551, 879733], [44475821, 22843831, 53802127, 33902551, 879733]], 'inner_hash': 798, 'inner_nilpotent': False, 'inner_order': 972, 'inner_split': True, 'inner_tex': 'C_3^3:S_3^2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 12], [2, 18], [4, 15], [6, 2], [12, 4]], 'label': '972.798', 'linC_count': 90, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 10, 'linQ_dim': 10, 'linQ_dim_count': 10, 'linR_count': 10, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^3:S3^2', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 51, 'number_divisions': 34, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 203, 'number_subgroup_classes': 340, 'number_subgroups': 3204, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 63], [3, 242], [6, 666]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [729001, 44469829, 729001], 'outer_gens': [[44475821, 22843831, 732529, 1097596, 879733], [44476649, 22849231, 732529, 879733, 1097596], [22605821, 22843831, 735229, 33902551, 53803441]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 9], [6, 2], [8, 6], [12, 2], [24, 1]], 'representations': {'PC': {'code': 13730692731309503197476112621618359, 'gens': [1, 3, 4, 6, 7], 'pres': [7, -2, -3, -3, -2, -3, -3, -3, 14, 1010, 450, 2523, 80, 2524, 9077, 530, 1791]}, 'GLZN': {'d': 2, 'p': 90, 'gens': [44469001, 1215931, 729829, 1096271, 879733, 1097596, 731701]}, 'Perm': {'d': 15, 'gens': [7, 13898309183, 19295141040, 325, 100602351360, 435, 194648877360]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:S_3^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 177407220
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 798, 'group_order': 972, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 729001, 'size': 1}
  • id: 177407231
    {'aut_label': '2A', 'centralizer': '9.a1.a1', 'counter': 2, 'group_counter': 798, 'group_order': 972, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 729829, 'size': 9}
  • id: 177407242
    {'aut_label': '2B', 'centralizer': '27.c1.a1', 'counter': 3, 'group_counter': 798, 'group_order': 972, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 735821, 'size': 27}
  • id: 177407253
    {'aut_label': '2B', 'centralizer': '27.c1.b1', 'counter': 4, 'group_counter': 798, 'group_order': 972, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 733949, 'size': 27}
  • id: 177407264
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 798, 'group_order': 972, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 734401, 'size': 2}
  • id: 177407267
    {'aut_label': '3B', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 798, 'group_order': 972, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 879733, 'size': 2}
  • id: 177407268
    {'aut_label': '3B', 'centralizer': '2.b1.b1', 'counter': 7, 'group_counter': 798, 'group_order': 972, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 33902551, 'size': 2}
  • id: 177407269
    {'aut_label': '3D1', 'centralizer': '3.c1.a1', 'counter': 8, 'group_counter': 798, 'group_order': 972, 'label': '3D1', 'order': 3, 'powers': [9, 1], 'representative': 22599001, 'size': 3}
  • id: 177407270
    {'aut_label': '3D1', 'centralizer': '3.c1.a1', 'counter': 9, 'group_counter': 798, 'group_order': 972, 'label': '3D-1', 'order': 3, 'powers': [8, 1], 'representative': 44469001, 'size': 3}
  • id: 177407221
    {'aut_label': '3E', 'centralizer': '4.a1.a1', 'counter': 10, 'group_counter': 798, 'group_order': 972, 'label': '3E', 'order': 3, 'powers': [10, 1], 'representative': 34045183, 'size': 4}
  • id: 177407222
    {'aut_label': '3F', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 798, 'group_order': 972, 'label': '3F', 'order': 3, 'powers': [11, 1], 'representative': 877033, 'size': 4}
  • id: 177407223
    {'aut_label': '3F', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 798, 'group_order': 972, 'label': '3G', 'order': 3, 'powers': [12, 1], 'representative': 33899851, 'size': 4}
  • id: 177407224
    {'aut_label': '3H1', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 798, 'group_order': 972, 'label': '3H1', 'order': 3, 'powers': [14, 1], 'representative': 34050583, 'size': 4}
  • id: 177407225
    {'aut_label': '3H1', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 798, 'group_order': 972, 'label': '3H-1', 'order': 3, 'powers': [13, 1], 'representative': 20635291, 'size': 4}
  • id: 177407226
    {'aut_label': '3I', 'centralizer': '6.b1.a1', 'counter': 15, 'group_counter': 798, 'group_order': 972, 'label': '3I', 'order': 3, 'powers': [15, 1], 'representative': 23091331, 'size': 6}
  • id: 177407227
    {'aut_label': '3J1', 'centralizer': '6.j1.a1', 'counter': 16, 'group_counter': 798, 'group_order': 972, 'label': '3J1', 'order': 3, 'powers': [17, 1], 'representative': 10060741, 'size': 6}
  • id: 177407228
    {'aut_label': '3J1', 'centralizer': '6.j1.a1', 'counter': 17, 'group_counter': 798, 'group_order': 972, 'label': '3J-1', 'order': 3, 'powers': [16, 1], 'representative': 44622433, 'size': 6}
  • id: 177407229
    {'aut_label': '3J1', 'centralizer': '6.j1.b1', 'counter': 18, 'group_counter': 798, 'group_order': 972, 'label': '3K1', 'order': 3, 'powers': [19, 1], 'representative': 55772551, 'size': 6}
  • id: 177407230
    {'aut_label': '3J1', 'centralizer': '6.j1.b1', 'counter': 19, 'group_counter': 798, 'group_order': 972, 'label': '3K-1', 'order': 3, 'powers': [18, 1], 'representative': 44837596, 'size': 6}
  • id: 177407232
    {'aut_label': '3L1', 'centralizer': '6.g1.a1', 'counter': 20, 'group_counter': 798, 'group_order': 972, 'label': '3L1', 'order': 3, 'powers': [21, 1], 'representative': 44713831, 'size': 6}
  • id: 177407233
    {'aut_label': '3L1', 'centralizer': '6.g1.a1', 'counter': 21, 'group_counter': 798, 'group_order': 972, 'label': '3L-1', 'order': 3, 'powers': [20, 1], 'representative': 1218631, 'size': 6}
  • id: 177407234
    {'aut_label': '3M', 'centralizer': '12.c1.a1', 'counter': 22, 'group_counter': 798, 'group_order': 972, 'label': '3M', 'order': 3, 'powers': [22, 1], 'representative': 22994473, 'size': 12}
  • id: 177407235
    {'aut_label': '3M', 'centralizer': '12.c1.a1', 'counter': 23, 'group_counter': 798, 'group_order': 972, 'label': '3N', 'order': 3, 'powers': [23, 1], 'representative': 56017381, 'size': 12}
  • id: 177407236
    {'aut_label': '3O1', 'centralizer': '12.c1.a1', 'counter': 24, 'group_counter': 798, 'group_order': 972, 'label': '3O1', 'order': 3, 'powers': [25, 1], 'representative': 55430923, 'size': 12}
  • id: 177407237
    {'aut_label': '3O1', 'centralizer': '12.c1.a1', 'counter': 25, 'group_counter': 798, 'group_order': 972, 'label': '3O-1', 'order': 3, 'powers': [24, 1], 'representative': 42744721, 'size': 12}
  • id: 177407238
    {'aut_label': '3P1', 'centralizer': '12.b1.a1', 'counter': 26, 'group_counter': 798, 'group_order': 972, 'label': '3P1', 'order': 3, 'powers': [27, 1], 'representative': 55915183, 'size': 12}
  • id: 177407239
    {'aut_label': '3P1', 'centralizer': '12.b1.a1', 'counter': 27, 'group_counter': 798, 'group_order': 972, 'label': '3P-1', 'order': 3, 'powers': [26, 1], 'representative': 12175183, 'size': 12}
  • id: 177407240
    {'aut_label': '3Q1', 'centralizer': '12.g1.a1', 'counter': 28, 'group_counter': 798, 'group_order': 972, 'label': '3Q1', 'order': 3, 'powers': [29, 1], 'representative': 44864473, 'size': 12}
  • id: 177407241
    {'aut_label': '3Q1', 'centralizer': '12.g1.a1', 'counter': 29, 'group_counter': 798, 'group_order': 972, 'label': '3Q-1', 'order': 3, 'powers': [28, 1], 'representative': 1124473, 'size': 12}
  • id: 177407243
    {'aut_label': '3Q1', 'centralizer': '12.g1.a1', 'counter': 30, 'group_counter': 798, 'group_order': 972, 'label': '3R1', 'order': 3, 'powers': [31, 1], 'representative': 12277381, 'size': 12}
  • id: 177407244
    {'aut_label': '3Q1', 'centralizer': '12.g1.a1', 'counter': 31, 'group_counter': 798, 'group_order': 972, 'label': '3R-1', 'order': 3, 'powers': [30, 1], 'representative': 34147381, 'size': 12}
  • id: 177407245
    {'aut_label': '3S1', 'centralizer': '12.g1.a1', 'counter': 32, 'group_counter': 798, 'group_order': 972, 'label': '3S1', 'order': 3, 'powers': [33, 1], 'representative': 11690923, 'size': 12}
  • id: 177407246
    {'aut_label': '3S1', 'centralizer': '12.g1.a1', 'counter': 33, 'group_counter': 798, 'group_order': 972, 'label': '3S-1', 'order': 3, 'powers': [32, 1], 'representative': 20874721, 'size': 12}
  • id: 177407247
    {'aut_label': '3S1', 'centralizer': '12.g1.a1', 'counter': 34, 'group_counter': 798, 'group_order': 972, 'label': '3T1', 'order': 3, 'powers': [35, 1], 'representative': 64614721, 'size': 12}
  • id: 177407248
    {'aut_label': '3S1', 'centralizer': '12.g1.a1', 'counter': 35, 'group_counter': 798, 'group_order': 972, 'label': '3T-1', 'order': 3, 'powers': [34, 1], 'representative': 33560923, 'size': 12}
  • id: 177407249
    {'aut_label': '6A', 'centralizer': '18.c1.a1', 'counter': 36, 'group_counter': 798, 'group_order': 972, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 732529, 'size': 18}
  • id: 177407250
    {'aut_label': '6B1', 'centralizer': '27.c1.a1', 'counter': 37, 'group_counter': 798, 'group_order': 972, 'label': '6B1', 'order': 6, 'powers': [8, 3], 'representative': 44475821, 'size': 27}
  • id: 177407251
    {'aut_label': '6B1', 'centralizer': '27.c1.a1', 'counter': 38, 'group_counter': 798, 'group_order': 972, 'label': '6B-1', 'order': 6, 'powers': [9, 3], 'representative': 22605821, 'size': 27}
  • id: 177407252
    {'aut_label': '6C1', 'centralizer': '27.a1.a1', 'counter': 39, 'group_counter': 798, 'group_order': 972, 'label': '6C1', 'order': 6, 'powers': [9, 2], 'representative': 22602529, 'size': 27}
  • id: 177407254
    {'aut_label': '6C1', 'centralizer': '27.a1.a1', 'counter': 40, 'group_counter': 798, 'group_order': 972, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 44472529, 'size': 27}
  • id: 177407255
    {'aut_label': '6B1', 'centralizer': '27.c1.b1', 'counter': 41, 'group_counter': 798, 'group_order': 972, 'label': '6D1', 'order': 6, 'powers': [8, 4], 'representative': 44473949, 'size': 27}
  • id: 177407256
    {'aut_label': '6B1', 'centralizer': '27.c1.b1', 'counter': 42, 'group_counter': 798, 'group_order': 972, 'label': '6D-1', 'order': 6, 'powers': [9, 4], 'representative': 22603949, 'size': 27}
  • id: 177407257
    {'aut_label': '6E', 'centralizer': '54.m1.a1', 'counter': 43, 'group_counter': 798, 'group_order': 972, 'label': '6E', 'order': 6, 'powers': [6, 3], 'representative': 9820931, 'size': 54}
  • id: 177407258
    {'aut_label': '6E', 'centralizer': '54.m1.b1', 'counter': 44, 'group_counter': 798, 'group_order': 972, 'label': '6F', 'order': 6, 'powers': [7, 4], 'representative': 1243394, 'size': 54}
  • id: 177407259
    {'aut_label': '6G', 'centralizer': '54.c1.a1', 'counter': 45, 'group_counter': 798, 'group_order': 972, 'label': '6G', 'order': 6, 'powers': [15, 2], 'representative': 55434154, 'size': 54}
  • id: 177407260
    {'aut_label': '6H1', 'centralizer': '54.m1.a1', 'counter': 46, 'group_counter': 798, 'group_order': 972, 'label': '6H1', 'order': 6, 'powers': [16, 3], 'representative': 1122233, 'size': 54}
  • id: 177407261
    {'aut_label': '6H1', 'centralizer': '54.m1.a1', 'counter': 47, 'group_counter': 798, 'group_order': 972, 'label': '6H-1', 'order': 6, 'powers': [17, 3], 'representative': 31449731, 'size': 54}
  • id: 177407262
    {'aut_label': '6H1', 'centralizer': '54.m1.b1', 'counter': 48, 'group_counter': 798, 'group_order': 972, 'label': '6I1', 'order': 6, 'powers': [18, 4], 'representative': 44834354, 'size': 54}
  • id: 177407263
    {'aut_label': '6H1', 'centralizer': '54.m1.b1', 'counter': 49, 'group_counter': 798, 'group_order': 972, 'label': '6I-1', 'order': 6, 'powers': [19, 4], 'representative': 55769399, 'size': 54}
  • id: 177407265
    {'aut_label': '6J1', 'centralizer': '54.d1.a1', 'counter': 50, 'group_counter': 798, 'group_order': 972, 'label': '6J1', 'order': 6, 'powers': [20, 2], 'representative': 33659914, 'size': 54}
  • id: 177407266
    {'aut_label': '6J1', 'centralizer': '54.d1.a1', 'counter': 51, 'group_counter': 798, 'group_order': 972, 'label': '6J-1', 'order': 6, 'powers': [21, 2], 'representative': 12274114, 'size': 54}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 18628579
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 18628590
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 18628601
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 18628607
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 18628608
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 18628609
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -2, 1, -1, 1, -1, 1, 1, -2, -1, -2, 1, 1, -1, 2, 1, 1], 'schur_index': 1}
  • id: 18628610
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -2, -1, 1, 1, 1, 1, -1, 2, 1, -2, -1, 1, 1, -2, 1, -1], 'schur_index': 1}
  • id: 18628611
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 1, 1, -1, 1, -1, 1, -2, 1, 2, 1, -1, 1, -2, -1, 1], 'schur_index': 1}
  • id: 18628612
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 18628580
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, -1, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 0, 2, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, -1], 'schur_index': 1}
  • id: 18628581
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 0, 2, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 18628582
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 18628583
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 0, 2, -1, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 0, -2, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 1], 'schur_index': 1}
  • id: 18628584
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, -2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 18628585
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, 1, -2, 1, 1, -2, 4, 1, -2, 1, -2, -2, 1, 1, 1, 1, -2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0], 'schur_index': 1}
  • id: 18628586
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2h', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 4, -2, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, 4, 1, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, 4, -2, -2, -2, 1, 1, 1, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, 1], 'schur_index': 1}
  • id: 18628587
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2i', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, -2, -2, 4, 4, 4, 4, 4, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, -2, -2, -2, -2, 1, 1, 1, -2, 1, 4, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 18628588
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2j', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, -2, -2, 4, 4, 4, 4, 4, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, -2, -2, -2, -2, 1, 1, 1, -2, 1, -4, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 18628589
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2k', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, -2, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, 4, 1, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, 4, -2, -2, -2, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, -1, 0, 0, 0, 0, -1], 'schur_index': 1}
  • id: 18628591
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.2l', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 0, 0, -4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, 1, -2, 1, 1, -2, 4, 1, -2, 1, -2, -2, 1, 1, 1, 1, -2, 0, 0, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0], 'schur_index': 1}
  • id: 18628592
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, -2, -2, 4, 4, 1, 1, 1, -2, -2, 4, 4, 4, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, -2, 1, -2, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628593
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, -2, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, 4, 4, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628594
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, -2, 4, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, -2, -2, 4, 1, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628602
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.6a', 'multiplicity': 1, 'nt': [9, 11], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, 6, 6, 0, 0, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628603
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.6b', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -3, 6, 6, 0, 0, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628595
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4d', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 2, -4, -4, -4, -4, 8, 2, 2, 2, 2, -1, -1, 2, -4, -1, 2, -1, -4, 2, 2, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628596
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4e', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, 8, -4, -4, -4, -4, -4, -4, 8, 2, 2, -4, 2, -4, -4, 2, -1, -1, -1, 2, -1, 2, 2, -4, 2, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628597
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4f', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 2, 2, -4, -4, 2, 2, -4, -1, -1, 2, -4, -1, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628598
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4g', 'multiplicity': 2, 'nt': [12, 71], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, -4, 8, 8, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -1, -1, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628599
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4h', 'multiplicity': 2, 'nt': [12, 130], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 2, -4, -4, 2, 2, -4, 2, 2, 2, 2, -4, 5, -1, 2, -4, -1, -1, 2, -1, -1, -1, 5, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628600
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.4i', 'multiplicity': 2, 'nt': [12, 130], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 2, -4, -4, 2, 2, -4, 2, 2, 2, 2, 5, -4, -1, 2, 5, -1, -1, 2, -1, -1, -1, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628604
    {'cdim': 12, 'counter': 32, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.12a', 'multiplicity': 1, 'nt': [18, 121], 'qdim': 12, 'qvalues': [12, 0, 0, 0, -6, -6, 12, 0, 0, -6, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628605
    {'cdim': 12, 'counter': 33, 'faithful': False, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.12b', 'multiplicity': 1, 'nt': [18, 121], 'qdim': 12, 'qvalues': [12, 0, 0, 0, -6, 12, -6, 0, 0, -6, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18628606
    {'cdim': 12, 'counter': 34, 'faithful': True, 'group': '972.798', 'group_order': 972, 'image': None, 'label': '972.798.12c', 'multiplicity': 2, 'nt': [36, 1525], 'qdim': 24, 'qvalues': [24, 0, 0, 0, -12, -12, -12, 0, 0, 6, -3, -3, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 39892864
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 972, 'label': '972.798.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39892875
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 486, 'label': '972.798.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 39892886
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 486, 'label': '972.798.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 39892897
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 486, 'label': '972.798.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 39892908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 324, 'label': '972.798.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 39892911
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 324, 'label': '972.798.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 39892912
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 162, 'label': '972.798.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 39892913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 162, 'label': '972.798.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 39892914
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 162, 'label': '972.798.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]]]}
  • id: 39892865
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 162, 'label': '972.798.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]]]}
  • id: 39892866
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 162, 'label': '972.798.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, -1]]]}
  • id: 39892867
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 972, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 162, 'label': '972.798.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, 1]]]}
  • id: 39892868
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1.b1', 'kernel_order': 162, 'label': '972.798.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892869
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1.a1', 'kernel_order': 162, 'label': '972.798.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 39892870
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 162, 'label': '972.798.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 39892871
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 81, 'label': '972.798.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 39892872
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 81, 'label': '972.798.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 39892873
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 81, 'label': '972.798.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892874
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 19, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.b1', 'kernel_order': 54, 'label': '972.798.2g1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892876
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 20, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.b1', 'kernel_order': 54, 'label': '972.798.2g2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892877
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 54, 'label': '972.798.2h1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]]]}
  • id: 39892878
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 54, 'label': '972.798.2h2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]]]}
  • id: 39892879
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 54, 'label': '972.798.2i1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]]]}
  • id: 39892880
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 54, 'label': '972.798.2i2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]]]}
  • id: 39892881
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 27, 'label': '972.798.2j1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]]]}
  • id: 39892882
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 162, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 27, 'label': '972.798.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]]]}
  • id: 39892883
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.b1', 'kernel_order': 27, 'label': '972.798.2k1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]]]}
  • id: 39892884
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 162, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.b1', 'kernel_order': 27, 'label': '972.798.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]]]}
  • id: 39892885
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 27, 'label': '972.798.2l1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892887
    {'center': '6.c1.b1', 'center_index': 6, 'center_order': 162, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 27, 'label': '972.798.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892888
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 27, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.d1.a1', 'kernel_order': 27, 'label': '972.798.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892889
    {'center': '36.a1.b1', 'center_index': 36, 'center_order': 27, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.b1', 'kernel_order': 27, 'label': '972.798.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892890
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 27, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 27, 'label': '972.798.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892891
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 27, 'counter': 34, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.c1.a1', 'kernel_order': 9, 'label': '972.798.4d1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892892
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 27, 'counter': 35, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.c1.a1', 'kernel_order': 9, 'label': '972.798.4d2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892893
    {'center': '36.a1.b1', 'center_index': 36, 'center_order': 27, 'counter': 36, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.b1', 'kernel_order': 9, 'label': '972.798.4e1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892894
    {'center': '36.a1.b1', 'center_index': 36, 'center_order': 27, 'counter': 37, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.b1', 'kernel_order': 9, 'label': '972.798.4e2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892895
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 27, 'counter': 38, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 9, 'label': '972.798.4f1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[4, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892896
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 27, 'counter': 39, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 9, 'label': '972.798.4f2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[4, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892898
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 40, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.40', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 9, 'label': '972.798.4g1', 'nt': [12, 71], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892899
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.40', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 9, 'label': '972.798.4g2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892900
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 42, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.167', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 3, 'label': '972.798.4h1', 'nt': [12, 130], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-3, 0], [-2, 1]], [[2, 0], [-1, 1]], [[1, -1]], [[1, 0]], [[-1, 0], [2, 1]], [[1, 0], [3, 1]], [[1, -1]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 1]], [[1, -1]], [[3, 0], [1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892901
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.167', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 3, 'label': '972.798.4h2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-1, 0], [2, 1]], [[3, 0], [1, 1]], [[1, 1]], [[1, 0]], [[-3, 0], [-2, 1]], [[-2, 0], [-3, 1]], [[1, 1]], [[1, 0]], [[1, 0], [3, 1]], [[1, -1]], [[1, 1]], [[2, 0], [-1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892902
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.167', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 3, 'label': '972.798.4i1', 'nt': [12, 130], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[3, 0], [1, 1]], [[-1, 0], [2, 1]], [[1, -1]], [[1, 0]], [[2, 0], [-1, 1]], [[-2, 0], [-3, 1]], [[1, -1]], [[1, 0]], [[1, 0], [3, 1]], [[1, 1]], [[1, -1]], [[-3, 0], [-2, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892903
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.167', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 3, 'label': '972.798.4i2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[2, 0], [-1, 1]], [[-3, 0], [-2, 1]], [[1, 1]], [[1, 0]], [[3, 0], [1, 1]], [[1, 0], [3, 1]], [[1, 1]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, -1]], [[1, 1]], [[-1, 0], [2, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892904
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 18, 'counter': 46, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '54.5', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1.a1', 'kernel_order': 18, 'label': '972.798.6a', 'nt': [9, 11], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892905
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 18, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.d1.a1', 'kernel_order': 9, 'label': '972.798.6b', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892906
    {'center': '324.b1.b1', 'center_index': 324, 'center_order': 3, 'counter': 48, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.116', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1.b1', 'kernel_order': 3, 'label': '972.798.12a', 'nt': [18, 121], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892907
    {'center': '324.b1.a1', 'center_index': 324, 'center_order': 3, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '324.116', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1.a1', 'kernel_order': 3, 'label': '972.798.12b', 'nt': [18, 121], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892909
    {'center': '972.a1.a1', 'center_index': 972, 'center_order': 1, 'counter': 50, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '972.798', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1.a1', 'kernel_order': 1, 'label': '972.798.12c1', 'nt': [36, 1525], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39892910
    {'center': '972.a1.a1', 'center_index': 972, 'center_order': 1, 'counter': 51, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '972.798', 'group_counter': 798, 'group_order': 972, 'image': None, 'image_isoclass': '972.798', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1.a1', 'kernel_order': 1, 'label': '972.798.12c2', 'nt': [36, 2], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  Showing the first 100 of 340 matching records in this table.
  • id: 275325998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 972, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '972.798.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.798', 'subgroup_hash': 798, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 486, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.231', 'subgroup_hash': 231, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.229', 'subgroup_hash': 229, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.229', 'subgroup_hash': 229, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.3.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 243, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '972.798.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 275325999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 275326010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 162, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 275326021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 275326110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 275326165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 275326176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.6.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.9.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 275326271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 275326273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 275326280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 54, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.798.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 275326311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.18.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 275326337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 275326000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.798', 'ambient_counter': 798, 'ambient_order': 972, 'ambient_tex': 'C_3^3:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.798.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
• gps_subgroup_data •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  Showing the first 100 of 340 matching records in this table.
  • id: 275325998
    {'ambient': '972.798', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': ['972.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4043, 4768, 5528, 4003, 6599, 4612, 6132, 5374], 'generators': [735821, 33902551, 734401, 729829, 879733, 22599001, 22843831], 'label': '972.798.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '972.798'}
  • id: 275325999
    {'ambient': '972.798', 'aut_centralizer_order': 9, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4686', 'aut_weyl_index': 9, 'centralizer': '108.b1.a1', 'complements': ['162.m1.a1', '162.n1.a1', '162.m1.b1', '162.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '18.a1.a1', '18.d1.a1', '18.d1.b1', '18.g1.a1', '18.j1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3916, 9358, 6165, 9560, 4282, 9029, 5656, 9278], 'generators': [729829, 879733, 22599001, 734401, 33902551], 'label': '972.798.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '972.798', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 275326000
    {'ambient': '972.798', 'aut_centralizer_order': 4, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.102', 'aut_weyl_index': 36, 'centralizer': '486.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.c1.a1', '9.c1.b1'], 'contains': ['54.c1.a1', '54.z1.a1', '54.z1.b1', '81.b1.a1', '81.c1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3045, -1, 5297, -1, 7730, -1, 6763, -1], 'generators': [735821, 729829, 22843831, 734401], 'label': '972.798.27.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.b1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 275326001
    {'ambient': '972.798', 'aut_centralizer_order': 12, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '162.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.d1.a1'], 'contains': ['54.g1.a1', '54.m1.a1', '54.q1.b1', '81.a1.a1', '81.d1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [86, -1, 8708, -1, 8996, -1, 8714, -1], 'generators': [735821, 729829, 22599001, 879733], 'label': '972.798.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '27.c1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326002
    {'ambient': '972.798', 'aut_centralizer_order': 12, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '162.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.b1', '9.d1.a1'], 'contains': ['54.g1.b1', '54.m1.b1', '54.q1.a1', '81.a1.a1', '81.d1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [86, -1, 7989, -1, 8996, -1, 8827, -1], 'generators': [735821, 729829, 22599001, 33902551], 'label': '972.798.27.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.b1', 'old_label': '27.c1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326003
    {'ambient': '972.798', 'aut_centralizer_order': 12, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.c1.a1', '9.e1.a1'], 'contains': ['54.e1.a1', '54.n1.a1', '54.y1.b1', '81.b1.a1', '81.d1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1539, -1, 6978, -1, 8343, -1, 6658, -1], 'generators': [735821, 729829, 734401, 879733], 'label': '972.798.27.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '27.d1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326004
    {'ambient': '972.798', 'aut_centralizer_order': 12, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.b1', '9.c1.b1', '9.e1.a1'], 'contains': ['54.e1.b1', '54.n1.b1', '54.y1.a1', '81.b1.a1', '81.d1.b1'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1539, -1, 5097, -1, 8343, -1, 6590, -1], 'generators': [735821, 729829, 734401, 33902551], 'label': '972.798.27.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '27.d1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326005
    {'ambient': '972.798', 'aut_centralizer_order': 4, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.f1.a1'], 'contains': ['54.h1.a1', '54.s1.a1', '54.bb1.b1', '81.c1.a1', '81.d1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1114, -1, 9609, -1, 9665, -1, 9328, -1], 'generators': [735821, 729829, 22843831, 879733], 'label': '972.798.27.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '27.e1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326006
    {'ambient': '972.798', 'aut_centralizer_order': 4, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.b1', '9.f1.a1'], 'contains': ['54.h1.b1', '54.s1.b1', '54.bb1.a1', '81.c1.a1', '81.d1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [1114, -1, 9955, -1, 9665, -1, 9260, -1], 'generators': [735821, 729829, 22843831, 33902551], 'label': '972.798.27.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.b1', 'old_label': '27.e1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326007
    {'ambient': '972.798', 'aut_centralizer_order': 12, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '9.e1.a1', '9.f1.a1'], 'contains': ['54.a1.a1', '54.v1.a1', '54.v1.b1', '81.d1.a1', '81.d1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [194, -1, 9392, -1, 9788, -1, 9191, -1], 'generators': [735821, 729829, 33902551, 879733], 'label': '972.798.27.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '27.f1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326008
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': ['27.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.d1.a1', '18.d1.a1', '18.m1.a1', '18.p1.b1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.f1.a1', '108.m1.a1', '108.u1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3544, 4727, 6386, 7015, 3939, 4681, 3184, 5340], 'generators': [22599001, 734401, 879733], 'label': '972.798.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['108.a1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '972.798', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326009
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': ['27.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.b1.a1', '12.d1.b1', '18.d1.b1', '18.m1.b1', '18.p1.a1'], 'contains': ['108.a1.b1', '108.b1.a1', '108.f1.b1', '108.m1.b1', '108.u1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3544, 4727, 3775, 6248, 3939, 4681, 3114, 6040], 'generators': [22599001, 734401, 33902551], 'label': '972.798.36.a1.b1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.b1', 'normal_contained_in': ['12.a1.b1', '12.b1.a1'], 'normal_contains': ['108.a1.b1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.b1', 'projective_image': '972.798', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326010
    {'ambient': '972.798', 'aut_centralizer_order': 9, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4686', 'aut_weyl_index': 9, 'centralizer': '108.c1.a1', 'complements': ['162.h1.a1', '162.i1.a1', '162.h1.b1', '162.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '18.e1.a1', '18.e1.b1', '18.h1.a1', '18.k1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4478, 6804, 6367, 7109, 4566, 6878, 6037, 7680], 'generators': [729829, 879733, 22843831, 734401, 33902551], 'label': '972.798.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '972.798', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 275326011
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': ['27.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.e1.a1', '18.b1.b1', '18.e1.a1', '18.q1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.h1.a1', '108.o1.a1', '108.bc1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5195, 3607, 6694, 5482, 5013, 3738, 5453, 3281], 'generators': [22843831, 734401, 879733], 'label': '972.798.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '12.c1.a1', '18.b1.b1'], 'normal_contains': ['108.a1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '972.798', 'quotient_action_image': '12.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 275326012
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': ['27.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.c1.a1', '12.e1.b1', '18.b1.a1', '18.e1.b1', '18.q1.b1'], 'contains': ['108.a1.b1', '108.c1.a1', '108.h1.b1', '108.o1.b1', '108.bc1.b1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5195, 3607, 4657, 3835, 5013, 3738, 5192, 4639], 'generators': [22843831, 734401, 33902551], 'label': '972.798.36.b1.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.b1', 'normal_contained_in': ['12.a1.b1', '12.c1.a1', '18.b1.a1'], 'normal_contains': ['108.a1.b1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.b1', 'projective_image': '972.798', 'quotient_action_image': '12.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 275326013
    {'ambient': '972.798', 'aut_centralizer_order': 486, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 486, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.g1.a1', '18.a1.a1', '18.t1.a1', '18.t1.b1'], 'contains': ['108.a1.a1', '108.a1.b1', '108.d1.a1', '108.e1.a1', '108.n1.a1', '108.n1.b1', '108.w1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4510, 5847, 6427, 7783, 3691, 5624, 3514, 6740], 'generators': [734401, 33902551, 879733], 'label': '972.798.36.c1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.a1.a1'], 'normal_contains': ['108.a1.b1', '108.a1.a1', '108.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '972.798', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 275326014
    {'ambient': '972.798', 'aut_centralizer_order': 216, 'aut_label': '36.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '18.a1.a1', 'complements': ['27.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.a1.b1', '12.h1.a1', '18.c1.a1', '18.u1.a1', '18.u1.b1'], 'contains': ['108.b1.a1', '108.c1.a1', '108.g1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6238, 2554, 3455, 4677, 2995, 2852, 2911, 3938], 'generators': [22599001, 22843831], 'label': '972.798.36.d1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.d1.a1', 'normal_contained_in': ['12.a1.b1', '12.a1.a1'], 'normal_contains': ['108.b1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '972.798', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326015
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '18.r1.b1'], 'contains': ['108.a1.a1', '108.f1.b1', '108.j1.a1', '108.p1.a1', '108.bd1.a1', '108.bd1.a2'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4249, -1, 6282, -1, 3318, -1, 3045, -1], 'generators': [55772551, 734401, 879733], 'label': '972.798.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.e1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326016
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.b1', '12.f1.b1', '18.r1.a1'], 'contains': ['108.a1.b1', '108.f1.a1', '108.j1.a1', '108.p1.b1', '108.bd1.b1', '108.bd1.b2'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4249, -1, 3375, -1, 3318, -1, 2593, -1], 'generators': [22749733, 734401, 33902551], 'label': '972.798.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.e1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326017
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '18.f1.a1'], 'contains': ['108.a1.a1', '108.g1.a1', '108.k1.a1', '108.q1.a1', '108.be1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8442, -1, 2951, -1, 1083, -1, 1300, -1], 'generators': [44713831, 734401, 879733], 'label': '972.798.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326018
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.f1.b1', '12.g1.a1', '18.f1.b1'], 'contains': ['108.a1.b1', '108.g1.a1', '108.k1.b1', '108.q1.b1', '108.be1.b1'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8442, -1, 2909, -1, 1083, -1, 979, -1], 'generators': [44713831, 734401, 33902551], 'label': '972.798.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.f1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326019
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.f1.a1', '18.s1.a1'], 'contains': ['108.a1.a1', '108.h1.b1', '108.i1.a1', '108.r1.a1', '108.bf1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4863, -1, 6344, -1, 3815, -1, 3583, -1], 'generators': [56017381, 734401, 879733], 'label': '972.798.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326020
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.b1', '12.f1.b1', '18.s1.b1'], 'contains': ['108.a1.b1', '108.h1.a1', '108.i1.a1', '108.r1.b1', '108.bf1.b1'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4863, -1, 4154, -1, 3815, -1, 3652, -1], 'generators': [22994473, 734401, 33902551], 'label': '972.798.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.g1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326021
    {'ambient': '972.798', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '324.b1.a1', 'complements': ['162.e1.a1', '162.f1.a1', '162.k1.b1', '162.l1.b1', '162.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.b1'], 'contains': ['12.a1.b1', '18.b1.a1', '18.p1.a1', '18.u1.a1', '18.v1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4328, 642, 4061, 440, 6076, 541, 3400, 4793], 'generators': [735821, 33902551, 22599001, 22843831, 734401], 'label': '972.798.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.b1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '972.798', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 275326022
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['108.a1.a1', '108.k1.b1', '108.l1.a1', '108.l1.b1', '108.s1.a1', '108.bg1.a1', '108.bg1.a2'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8025, -1, 1893, -1, 1207, -1, 719, -1], 'generators': [12277381, 734401, 879733], 'label': '972.798.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326023
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.e1.b1', '12.f1.b1', '12.g1.a1'], 'contains': ['108.a1.b1', '108.k1.a1', '108.l1.a1', '108.l1.b1', '108.s1.b1', '108.bg1.b1', '108.bg1.b2'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8025, -1, 1267, -1, 1207, -1, 650, -1], 'generators': [44864473, 734401, 33902551], 'label': '972.798.36.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.h1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326024
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.h1.a1', '12.i1.a1', '18.g1.a1'], 'contains': ['108.b1.a1', '108.e1.a1', '108.j1.a1', '108.t1.a1', '108.v1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5883, -1, 3934, -1, 2754, -1, 2662, -1], 'generators': [22599001, 734401, 34045183], 'label': '972.798.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326025
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.b1', '12.i1.a1', '18.v1.b1'], 'contains': ['108.b1.a1', '108.h1.a1', '108.k1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6085, -1, 3067, -1, 2528, -1, 2528, -1], 'generators': [22599001, 22994473], 'label': '972.798.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.j1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326026
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.d1.a1', '12.i1.a1', '18.v1.a1'], 'contains': ['108.b1.a1', '108.h1.b1', '108.k1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6085, -1, 2870, -1, 2528, -1, 2215, -1], 'generators': [22599001, 56017381], 'label': '972.798.36.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.j1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326027
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.d1.b1', '12.h1.a1', '12.i1.a1'], 'contains': ['108.b1.a1', '108.i1.a1', '108.l1.a1', '108.l1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7165, -1, 1781, -1, 2076, -1, 1972, -1], 'generators': [22599001, 55430923], 'label': '972.798.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326028
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.h1.a1', '12.j1.a1', '18.h1.a1'], 'contains': ['108.c1.a1', '108.e1.a1', '108.i1.a1', '108.x1.a1', '108.bh1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6785, -1, 4874, -1, 3442, -1, 5123, -1], 'generators': [22843831, 734401, 34045183], 'label': '972.798.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326029
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.j1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['108.e1.a1', '108.f1.a1', '108.f1.b1', '108.j1.a1', '108.y1.a1', '108.bi1.a1', '108.bi1.a2'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6867, -1, 3416, -1, 2411, -1, 2281, -1], 'generators': [22749733, 734401, 34045183], 'label': '972.798.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.m1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326030
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.k1.a1', '18.i1.a1'], 'contains': ['108.e1.a1', '108.g1.a1', '108.l1.a1', '108.z1.a1', '108.bj1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8568, -1, 3203, -1, 628, -1, 1231, -1], 'generators': [44713831, 734401, 34045183], 'label': '972.798.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326031
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.k1.b1', '18.i1.b1'], 'contains': ['108.e1.a1', '108.g1.a1', '108.l1.b1', '108.z1.b1', '108.bj1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8568, -1, 3007, -1, 628, -1, 910, -1], 'generators': [44713831, 734401, 20637991], 'label': '972.798.36.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.n1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326032
    {'ambient': '972.798', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '324.b1.b1', 'complements': ['162.e1.b1', '162.f1.a1', '162.k1.a1', '162.l1.a1', '162.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.b1.b1', '18.p1.b1', '18.u1.b1', '18.v1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4328, 642, 5169, 5360, 6076, 541, 6869, 402], 'generators': [733949, 879733, 22599001, 22843831, 734401], 'label': '972.798.6.c1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.b1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['12.a1.a1', '18.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '972.798', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 275326033
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.i1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['108.e1.a1', '108.h1.a1', '108.h1.b1', '108.i1.a1', '108.ba1.a1', '108.bk1.a1', '108.bk1.a2'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6949, -1, 4113, -1, 2878, -1, 2731, -1], 'generators': [22994473, 734401, 34045183], 'label': '972.798.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.o1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326034
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['108.e1.a1', '108.k1.a1', '108.k1.b1', '108.l1.a1', '108.bb1.a1', '108.bl1.a1', '108.bl1.a2'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8107, -1, 940, -1, 958, -1, 581, -1], 'generators': [44864473, 734401, 20637991], 'label': '972.798.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326035
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.j1.a1', '12.k1.b1'], 'contains': ['108.e1.a1', '108.k1.a1', '108.k1.b1', '108.l1.b1', '108.bb1.b1', '108.bl1.b1', '108.bl1.b2'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8107, -1, 744, -1, 958, -1, 511, -1], 'generators': [44864473, 734401, 34045183], 'label': '972.798.36.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.p1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326036
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.e1.b1', '12.j1.a1', '18.w1.a1'], 'contains': ['108.c1.a1', '108.f1.a1', '108.k1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6158, -1, 1853, -1, 2637, -1, 2155, -1], 'generators': [22749733, 22843831], 'label': '972.798.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.q1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326037
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.e1.a1', '12.j1.a1', '18.w1.b1'], 'contains': ['108.c1.a1', '108.f1.b1', '108.k1.b1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6158, -1, 2833, -1, 2637, -1, 2345, -1], 'generators': [55772551, 22843831], 'label': '972.798.36.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.q1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326038
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.e1.b1', '12.h1.a1', '12.j1.a1'], 'contains': ['108.c1.a1', '108.j1.a1', '108.l1.a1', '108.l1.b1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7091, -1, 1610, -1, 2185, -1, 1912, -1], 'generators': [55915183, 22843831], 'label': '972.798.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326039
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.f1.b1', '12.k1.a1', '12.k1.b1'], 'contains': ['108.f1.a1', '108.g1.a1', '108.h1.a1', '108.k1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7868, -1, 1552, -1, 1857, -1, 1851, -1], 'generators': [22749733, 22994473], 'label': '972.798.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326040
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.f1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['108.f1.b1', '108.g1.a1', '108.h1.b1', '108.k1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7868, -1, 2456, -1, 1857, -1, 1790, -1], 'generators': [55772551, 56017381], 'label': '972.798.36.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.s1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326041
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.b1', '12.k1.a1', '18.x1.a1'], 'contains': ['108.f1.a1', '108.h1.b1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6580, -1, 1743, -1, 2294, -1, 2094, -1], 'generators': [22749733, 56017381], 'label': '972.798.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.t1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326042
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.b1', '12.k1.b1', '18.x1.b1'], 'contains': ['108.f1.a1', '108.h1.b1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6580, -1, 1669, -1, 2294, -1, 2033, -1], 'generators': [10063441, 56017381], 'label': '972.798.36.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.t1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326043
    {'ambient': '972.798', 'aut_centralizer_order': 3, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1296.2985', 'aut_weyl_index': 6, 'centralizer': '324.b1.a1', 'complements': ['162.b1.a1', '162.d1.a1', '162.h1.b1', '162.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '18.b1.a1', '18.q1.a1', '18.s1.a1', '18.t1.a1', '18.y1.a1', '18.z1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3559, 2691, 6470, 1843, 8099, 2266, 5304, 6074], 'generators': [735821, 33902551, 879733, 22843831, 734401], 'label': '972.798.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '972.798', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 275326044
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.e1.a1', '12.k1.a1', '18.x1.c1'], 'contains': ['108.f1.b1', '108.h1.a1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6580, -1, 2795, -1, 2294, -1, 2467, -1], 'generators': [55772551, 22994473], 'label': '972.798.36.t1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.t1.c1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326045
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.e1.a1', '12.k1.b1', '18.x1.d1'], 'contains': ['108.f1.b1', '108.h1.a1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6580, -1, 2736, -1, 2294, -1, 2406, -1], 'generators': [55772551, 9579271], 'label': '972.798.36.t1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '36.t1.d1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.d1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 275326046
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.f1.b1', '12.j1.a1', '12.k1.a1'], 'contains': ['108.f1.a1', '108.i1.a1', '108.k1.b1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7474, -1, 980, -1, 1639, -1, 1365, -1], 'generators': [10063441, 55430923], 'label': '972.798.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.u1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326047
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.f1.b1', '12.j1.a1', '12.k1.b1'], 'contains': ['108.f1.a1', '108.i1.a1', '108.k1.b1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7474, -1, 900, -1, 1639, -1, 1044, -1], 'generators': [22749733, 55430923], 'label': '972.798.36.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.u1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326048
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.f1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['108.f1.b1', '108.i1.a1', '108.k1.a1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7474, -1, 1190, -1, 1639, -1, 1729, -1], 'generators': [55772551, 42744721], 'label': '972.798.36.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.u1.c1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326049
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.f1.a1', '12.j1.a1', '12.k1.b1'], 'contains': ['108.f1.b1', '108.i1.a1', '108.k1.a1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7474, -1, 1049, -1, 1639, -1, 1608, -1], 'generators': [55772551, 55430923], 'label': '972.798.36.u1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.u1.d1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.d1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326050
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.f1.b1', '12.h1.a1', '12.k1.a1'], 'contains': ['108.g1.a1', '108.i1.a1', '108.j1.a1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7948, -1, 1817, -1, 1530, -1, 1669, -1], 'generators': [55915183, 55430923], 'label': '972.798.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.v1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326051
    {'ambient': '972.798', 'aut_centralizer_order': 54, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.f1.b1', '12.h1.a1', '12.k1.b1'], 'contains': ['108.g1.a1', '108.i1.a1', '108.j1.a1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7948, -1, 1475, -1, 1530, -1, 1547, -1], 'generators': [42507991, 42744721], 'label': '972.798.36.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.v1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326052
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.b1', '12.i1.a1', '12.k1.a1'], 'contains': ['108.h1.a1', '108.j1.a1', '108.k1.b1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7796, -1, 1228, -1, 1748, -1, 1425, -1], 'generators': [55915183, 9579271], 'label': '972.798.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.w1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326053
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.b1', '12.i1.a1', '12.k1.b1'], 'contains': ['108.h1.a1', '108.j1.a1', '108.k1.b1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7796, -1, 1154, -1, 1748, -1, 1105, -1], 'generators': [55915183, 22994473], 'label': '972.798.36.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.w1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326054
    {'ambient': '972.798', 'aut_centralizer_order': 3, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1296.2985', 'aut_weyl_index': 6, 'centralizer': '324.b1.b1', 'complements': ['162.b1.a1', '162.d1.a1', '162.h1.a1', '162.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.c1.a1', '18.b1.b1', '18.q1.b1', '18.s1.b1', '18.t1.b1', '18.y1.b1', '18.z1.b1'], 'core': '6.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3559, 2691, 7083, 3957, 8099, 2266, 7798, 1683], 'generators': [733949, 879733, 33902551, 22843831, 734401], 'label': '972.798.6.d1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.b1', 'normal_contained_in': ['2.b1.b1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '18.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '972.798', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 275326055
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.f1.a1', '12.i1.a1', '12.k1.a1'], 'contains': ['108.h1.b1', '108.j1.a1', '108.k1.a1', '108.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7796, -1, 1101, -1, 1748, -1, 1486, -1], 'generators': [42507991, 56017381], 'label': '972.798.36.w1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.w1.c1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326056
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 432, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.f1.a1', '12.i1.a1', '12.k1.b1'], 'contains': ['108.h1.b1', '108.j1.a1', '108.k1.a1', '108.l1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7796, -1, 864, -1, 1748, -1, 1166, -1], 'generators': [55915183, 56017381], 'label': '972.798.36.w1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.w1.d1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.d1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326057
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.f1.b1', '12.i1.a1', '12.j1.a1'], 'contains': ['108.i1.a1', '108.j1.a1', '108.k1.a1', '108.k1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7374, -1, 705, -1, 1967, -1, 845, -1], 'generators': [42507991, 55430923], 'label': '972.798.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.x1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326058
    {'ambient': '972.798', 'aut_centralizer_order': 27, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.f1.b1', '12.i1.a1', '12.j1.a1'], 'contains': ['108.i1.a1', '108.j1.a1', '108.k1.a1', '108.k1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7374, -1, 668, -1, 1967, -1, 784, -1], 'generators': [55915183, 42744721], 'label': '972.798.36.x1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.x1.a2', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 275326059
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.n1.a1'], 'contains': ['108.m1.a1', '108.n1.a1', '108.p1.a1', '108.u1.b1', '108.v1.a1', '108.bd1.b1', '108.bd1.b2', '108.bi1.a1', '108.bi1.a2'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2273, -1, 4195, -1, 4682, -1, 3253, -1], 'generators': [22599001, 33899851, 879733], 'label': '972.798.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '36.y1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326060
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.n1.b1'], 'contains': ['108.m1.b1', '108.n1.b1', '108.p1.b1', '108.u1.a1', '108.v1.a1', '108.bd1.a1', '108.bd1.a2', '108.bi1.a1', '108.bi1.a2'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2273, -1, 6528, -1, 4682, -1, 3721, -1], 'generators': [22599001, 877033, 33902551], 'label': '972.798.36.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '36.y1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326061
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.y1.a1'], 'contains': ['108.n1.a1', '108.o1.a1', '108.r1.a1', '108.bc1.b1', '108.bf1.b1', '108.bh1.a1', '108.bk1.a1', '108.bk1.a2'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3664, -1, 8402, -1, 5730, -1, 7256, -1], 'generators': [22843831, 33899851, 879733], 'label': '972.798.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.z1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326062
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.y1.b1'], 'contains': ['108.n1.b1', '108.o1.b1', '108.r1.b1', '108.bc1.a1', '108.bf1.a1', '108.bh1.a1', '108.bk1.a1', '108.bk1.a2'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3664, -1, 8637, -1, 5730, -1, 7549, -1], 'generators': [22843831, 877033, 33902551], 'label': '972.798.36.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.z1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326063
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['108.n1.a1', '108.q1.a1', '108.s1.a1', '108.be1.b1', '108.bg1.b1', '108.bg1.b2', '108.bj1.a1', '108.bj1.b1', '108.bl1.a1', '108.bl1.a2', '108.bl1.b1', '108.bl1.b2'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9224, -1, 2269, -1, 173, -1, 165, -1], 'generators': [44713831, 33899851, 879733], 'label': '972.798.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.ba1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326064
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['108.n1.b1', '108.q1.b1', '108.s1.b1', '108.be1.a1', '108.bg1.a1', '108.bg1.a2', '108.bj1.a1', '108.bj1.b1', '108.bl1.a1', '108.bl1.a2', '108.bl1.b1', '108.bl1.b2'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9224, -1, 1935, -1, 173, -1, 373, -1], 'generators': [44713831, 877033, 33902551], 'label': '972.798.36.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.ba1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326065
    {'ambient': '972.798', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5344, -1, 6068, -1, 3938, -1, 5143, -1], 'generators': [729829, 879733, 22599001, 22843831, 734401], 'label': '972.798.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 275326066
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 486, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.j1.a1', '18.o1.a1', '18.o1.b1'], 'contains': ['108.d1.a1', '108.m1.a1', '108.m1.b1', '108.p1.a1', '108.p1.b1', '108.t1.a1', '108.y1.a1'], 'core': '108.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2001, -1, 6851, -1, 5137, -1, 5522, -1], 'generators': [22599001, 33902551, 879733], 'label': '972.798.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bb1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 275326067
    {'ambient': '972.798', 'aut_centralizer_order': 162, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 486, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.k1.a1', '18.z1.a1', '18.z1.b1'], 'contains': ['108.d1.a1', '108.o1.a1', '108.o1.b1', '108.r1.a1', '108.r1.b1', '108.x1.a1', '108.ba1.a1'], 'core': '108.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2511, -1, 9179, -1, 5854, -1, 8493, -1], 'generators': [22843831, 33902551, 879733], 'label': '972.798.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 275326068
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 486, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.l1.a1'], 'contains': ['108.d1.a1', '108.q1.a1', '108.q1.b1', '108.s1.a1', '108.s1.b1', '108.z1.a1', '108.z1.b1', '108.bb1.a1', '108.bb1.b1'], 'core': '108.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9740, -1, 3280, -1, 297, -1, 442, -1], 'generators': [44713831, 33902551, 879733], 'label': '972.798.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.bd1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326069
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['108.t1.a1', '108.u1.a1', '108.u1.b1', '108.v1.a1', '108.w1.a1', '108.y1.a1', '108.bd1.a1', '108.bd1.a2', '108.bd1.b1', '108.bd1.b2', '108.bi1.a1', '108.bi1.a2'], 'core': '972.a1.a1', 'coset_action_label': '36T1545', 'count': 12, 'diagramx': [3386, -1, 5476, -1, 3566, -1, 2976, -1], 'generators': [22599001, 877033, 34045183], 'label': '972.798.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.be1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326070
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['108.w1.a1', '108.x1.a1', '108.ba1.a1', '108.bc1.a1', '108.bc1.b1', '108.bf1.a1', '108.bf1.b1', '108.bh1.a1', '108.bk1.a1', '108.bk1.a2'], 'core': '972.a1.a1', 'coset_action_label': '36T1525', 'count': 12, 'diagramx': [5075, -1, 8578, -1, 5262, -1, 7325, -1], 'generators': [22843831, 877033, 34045183], 'label': '972.798.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '36.bf1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326071
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['108.w1.a1', '108.z1.b1', '108.bb1.a1', '108.be1.a1', '108.be1.b1', '108.bg1.a1', '108.bg1.a2', '108.bg1.b1', '108.bg1.b2', '108.bj1.a1', '108.bl1.b1', '108.bl1.b2'], 'core': '972.a1.a1', 'coset_action_label': '36T1576', 'count': 12, 'diagramx': [9107, -1, 2347, -1, 49, -1, 235, -1], 'generators': [44713831, 877033, 20637991], 'label': '972.798.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.bg1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326072
    {'ambient': '972.798', 'aut_centralizer_order': 81, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['108.w1.a1', '108.z1.a1', '108.bb1.b1', '108.be1.a1', '108.be1.b1', '108.bg1.a1', '108.bg1.a2', '108.bg1.b1', '108.bg1.b2', '108.bj1.b1', '108.bl1.a1', '108.bl1.a2'], 'core': '972.a1.a1', 'coset_action_label': '36T1576', 'count': 12, 'diagramx': [9107, -1, 2017, -1, 49, -1, 304, -1], 'generators': [44713831, 877033, 34045183], 'label': '972.798.36.bg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.bg1.a2', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 275326073
    {'ambient': '972.798', 'aut_centralizer_order': 108, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '36.d1.a1', 'complements': ['18.u1.a1', '18.w1.a1', '18.v1.a1', '18.x1.a1', '18.x1.b1', '18.u1.b1', '18.v1.b1', '18.w1.b1', '18.x1.c1', '18.x1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '27.f1.a1'], 'contains': ['108.d1.a1', '162.e1.a1', '162.e1.b1', '162.f1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2887, 7185, 9001, 8709, 5394, 6832, 8192, 7663], 'generators': [729829, 33902551, 879733], 'label': '972.798.54.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '972.798', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 275326074
    {'ambient': '972.798', 'aut_centralizer_order': 72, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.d1.a1', '18.d1.b1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '162.a1.a1', '162.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4988, -1, 5873, -1, 4105, -1, 5844, -1], 'generators': [729829, 22599001, 734401], 'label': '972.798.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326075
    {'ambient': '972.798', 'aut_centralizer_order': 72, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.e1.a1', '18.e1.b1', '18.h1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '162.a1.a1', '162.c1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5710, -1, 6082, -1, 4311, -1, 6187, -1], 'generators': [729829, 22843831, 734401], 'label': '972.798.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 275326076
    {'ambient': '972.798', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['12.a1.b1', '18.c1.a1', '18.d1.b1', '18.e1.b1', '18.f1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5344, -1, 5590, -1, 3938, -1, 4981, -1], 'generators': [729829, 33902551, 22599001, 22843831, 734401], 'label': '972.798.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '6.e1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 275326077
    {'ambient': '972.798', 'aut_centralizer_order': 72, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.f1.a1', '18.f1.b1', '18.i1.a1', '18.i1.b1'], 'contains': ['108.g1.a1', '162.a1.a1', '162.d1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8795, -1, 5943, -1, 1372, -1, 4688, -1], 'generators': [729829, 44713831, 734401], 'label': '972.798.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '54.d1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 275326078
    {'ambient': '972.798', 'aut_centralizer_order': 108, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1', '27.d1.a1'], 'contains': ['108.a1.a1', '162.a1.a1', '162.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4700, -1, 6768, -1, 4848, -1, 6073, -1], 'generators': [729829, 734401, 879733], 'label': '972.798.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.e1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326079
    {'ambient': '972.798', 'aut_centralizer_order': 108, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.d1.b1', '18.e1.b1', '18.f1.b1', '27.d1.b1'], 'contains': ['108.a1.b1', '162.a1.a1', '162.e1.b1'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4700, -1, 6013, -1, 4848, -1, 5959, -1], 'generators': [729829, 734401, 33902551], 'label': '972.798.54.e1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '54.e1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326080
    {'ambient': '972.798', 'aut_centralizer_order': 108, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.i1.b1'], 'contains': ['108.e1.a1', '162.a1.a1', '162.f1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5960, -1, 6152, -1, 3152, -1, 5361, -1], 'generators': [729829, 734401, 34045183], 'label': '972.798.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '54.f1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326081
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.j1.a1', '27.c1.a1'], 'contains': ['108.m1.a1', '162.b1.a1', '162.e1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1476, -1, 8943, -1, 6020, -1, 7982, -1], 'generators': [729829, 22599001, 879733], 'label': '972.798.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.g1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326082
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.j1.a1', '27.c1.b1'], 'contains': ['108.m1.b1', '162.b1.a1', '162.e1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1476, -1, 8873, -1, 6020, -1, 8097, -1], 'generators': [729829, 22599001, 33902551], 'label': '972.798.54.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '54.g1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326083
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.k1.a1', '27.e1.a1'], 'contains': ['108.o1.a1', '162.c1.a1', '162.e1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1879, -1, 9757, -1, 6224, -1, 9271, -1], 'generators': [729829, 22843831, 879733], 'label': '972.798.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.h1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326084
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.b1', '18.k1.a1', '27.e1.b1'], 'contains': ['108.o1.b1', '162.c1.a1', '162.e1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1879, -1, 9984, -1, 6224, -1, 9044, -1], 'generators': [729829, 22843831, 33902551], 'label': '972.798.54.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.b1', 'old_label': '54.h1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326085
    {'ambient': '972.798', 'aut_centralizer_order': 18, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.l1.a1'], 'contains': ['108.q1.a1', '162.d1.a1', '162.e1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9653, -1, 7023, -1, 793, -1, 4917, -1], 'generators': [729829, 44713831, 879733], 'label': '972.798.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '54.i1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326086
    {'ambient': '972.798', 'aut_centralizer_order': 18, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.b1', '18.l1.a1'], 'contains': ['108.q1.b1', '162.d1.a1', '162.e1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9653, -1, 6954, -1, 793, -1, 5031, -1], 'generators': [729829, 44713831, 33902551], 'label': '972.798.54.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.b1', 'old_label': '54.i1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326087
    {'ambient': '972.798', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.h1.a1', '18.c1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.i1.b1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6429, -1, 5687, -1, 3591, -1, 4819, -1], 'generators': [729829, 34045183, 22599001, 22843831, 734401], 'label': '972.798.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '6.f1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
  • id: 275326088
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.j1.a1'], 'contains': ['108.t1.a1', '162.b1.a1', '162.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3326, -1, 7945, -1, 4517, -1, 6302, -1], 'generators': [729829, 22599001, 34045183], 'label': '972.798.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '54.j1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326089
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.k1.a1'], 'contains': ['108.x1.a1', '162.c1.a1', '162.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4162, -1, 9223, -1, 5565, -1, 8288, -1], 'generators': [729829, 22843831, 34045183], 'label': '972.798.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '54.k1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326090
    {'ambient': '972.798', 'aut_centralizer_order': 18, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.l1.a1'], 'contains': ['108.z1.a1', '162.d1.a1', '162.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9941, -1, 7161, -1, 462, -1, 4574, -1], 'generators': [729829, 44713831, 34045183], 'label': '972.798.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '54.l1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326091
    {'ambient': '972.798', 'aut_centralizer_order': 18, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.b1', '18.l1.a1'], 'contains': ['108.z1.b1', '162.d1.a1', '162.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9941, -1, 7093, -1, 462, -1, 4460, -1], 'generators': [729829, 44713831, 20637991], 'label': '972.798.54.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '54.l1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326092
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '54.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.n1.a1', '18.o1.a1', '27.c1.a1'], 'contains': ['108.m1.a1', '162.g1.a1', '162.h1.a1', '162.i1.a1'], 'core': '324.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [270, -1, 7231, -1, 8183, -1, 5614, -1], 'generators': [735821, 22599001, 879733], 'label': '972.798.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.m1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326093
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '54.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '18.n1.b1', '18.o1.b1', '27.c1.b1'], 'contains': ['108.m1.b1', '162.g1.b1', '162.h1.b1', '162.i1.b1'], 'core': '324.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [270, -1, 8111, -1, 8183, -1, 8929, -1], 'generators': [733949, 22599001, 33902551], 'label': '972.798.54.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.b1', 'old_label': '54.m1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 275326094
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.q1.a1', '18.s1.a1', '18.t1.a1', '27.d1.a1'], 'contains': ['108.a1.a1', '162.g1.a1', '162.j1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2683, -1, 6679, -1, 7773, -1, 4232, -1], 'generators': [735821, 879733, 734401], 'label': '972.798.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.n1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326095
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '18.q1.b1', '18.s1.b1', '18.t1.b1', '27.d1.b1'], 'contains': ['108.a1.b1', '162.g1.b1', '162.j1.b1'], 'core': '108.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [2683, -1, 4585, -1, 7773, -1, 6860, -1], 'generators': [733949, 33902551, 734401], 'label': '972.798.54.n1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '54.n1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 275326096
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.p1.a1', '18.u1.a1', '18.v1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '162.h1.a1', '162.j1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2999, -1, 3868, -1, 6634, -1, 3422, -1], 'generators': [735821, 22599001, 734401], 'label': '972.798.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.o1.a1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 275326097
    {'ambient': '972.798', 'aut_centralizer_order': 36, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '54.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '18.p1.b1', '18.u1.b1', '18.v1.b1', '27.a1.a1'], 'contains': ['108.b1.a1', '162.h1.b1', '162.j1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2999, -1, 4410, -1, 6634, -1, 6478, -1], 'generators': [733949, 22599001, 734401], 'label': '972.798.54.o1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '54.o1.b1', 'projective_image': '972.798', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}